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[Algorithms I] Week 2-1 Stacks and Queues
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目录
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<div id="toc"><ul><li><a class="toc-href" href="#1-stacks" title="1. Stacks">1. Stacks</a><ul><li><a class="toc-href" href="#implementation-1-using-a-linkedlist" title="implementation 1: using a linkedlist">implementation 1: using a linkedlist</a></li><li><a class="toc-href" href="#array-implementation" title="array implementation">array implementation</a></li></ul></li><li><a class="toc-href" href="#2-resizing-arrays_1" title="2. Resizing Arrays">2. Resizing Arrays</a><ul><li><a class="toc-href" href="#resizing-strategy" title="resizing strategy">resizing strategy</a></li><li><a class="toc-href" href="#comparison-resizable-array-vs-linkedlist" title="comparison: resizable array vs linkedlist">comparison: resizable array vs linkedlist</a></li><li><a class="toc-href" href="#3-queues_1" title="3. Queues">3. Queues</a><ul><li><a class="toc-href" href="#linked-list-implementation" title="linked list implementation">linked list implementation</a></li><li><a class="toc-href" href="#resizing-array-implementation" title="resizing array implementation">resizing array implementation</a></li></ul></li></ul></li><li><a class="toc-href" href="#4-generics_2" title="4. Generics">4. Generics</a><ul><li><a class="toc-href" href="#a-pb-with-array-implementation" title="a pb with array implementation">a pb with array implementation</a></li><li><a class="toc-href" href="#autoboxing-for-primitive-types" title="autoboxing for primitive types">autoboxing for primitive types</a></li></ul></li><li><a class="toc-href" href="#5-iterators_1" title="5. Iterators">5. Iterators</a><ul><li><a class="toc-href" href="#interface" title="Interface">Interface</a></li><li><a class="toc-href" href="#bag-data-structure" title="Bag data structure">Bag data structure</a></li></ul></li><li><a class="toc-href" href="#6-applications_1" title="6. Applications">6. Applications</a><ul><li><a class="toc-href" href="#java-collections-library" title="Java collections library">Java collections library</a></li><li><a class="toc-href" href="#stacks-applications" title="Stacks applications">Stacks applications</a></li></ul></li></ul></div>
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</div>
<p>fundamental data types: stacks and queues
operations:
<strong>insert, remove, test empy, iterate,</strong>... <br/>
<img alt="" class="img-responsive" src="../images/algoI_week2_1/pasted_image.png"/> </p>
<p>module programming: seperate interface and implementation</p>
<h1 id="1-stacks">1. Stacks</h1>
<p>ex. a stack of strings</p>
<ul>
<li>
<p>API: </p>
<p>public interface StackoOfStrings{
void push(String item);
String pop();
boolean isEmpty();
//int size();
}</p>
</li>
</ul>
<h3 id="implementation-1-using-a-linkedlist">implementation 1: using a linkedlist</h3>
<p>insert/remove from the top of the linkedlist</p>
<ul>
<li>
<p>inner class</p>
<div class="highlight"><pre><span class="code-line"><span></span><span class="err">class ListNode{</span></span>
<span class="code-line"><span class="err"> String item;</span></span>
<span class="code-line"><span class="err"> ListNode next;</span></span>
<span class="code-line"><span class="err">}</span></span>
</pre></div>
</li>
<li>
<p>implementation </p>
<div class="highlight"><pre><span class="code-line"><span></span><span class="k">public</span> <span class="k">class</span> <span class="n">LinkedStackOfStrings</span> <span class="n">implements</span> <span class="n">StackoOfStrings</span><span class="err">{</span></span>
<span class="code-line"> <span class="k">class</span> <span class="n">Node</span><span class="err">{</span></span>
<span class="code-line"> <span class="n">String</span> <span class="n">item</span><span class="p">;</span></span>
<span class="code-line"> <span class="n">Node</span> <span class="k">next</span><span class="p">;</span></span>
<span class="code-line"> <span class="n">Node</span><span class="p">(</span><span class="n">String</span> <span class="n">item</span><span class="p">,</span> <span class="n">ListNode</span> <span class="n">nxt</span><span class="p">)</span><span class="err">{</span><span class="p">...</span><span class="err">}</span></span>
<span class="code-line"> <span class="err">}</span></span>
<span class="code-line"> <span class="n">private</span> <span class="n">Node</span> <span class="k">first</span><span class="p">;</span></span>
<span class="code-line"></span>
<span class="code-line"> <span class="k">public</span> <span class="n">LinkedStackOfStrings</span><span class="p">()</span><span class="err">{</span></span>
<span class="code-line"> <span class="k">first</span> <span class="o">=</span> <span class="k">null</span><span class="p">;</span></span>
<span class="code-line"> <span class="err">}</span></span>
<span class="code-line"> <span class="k">public</span> <span class="n">void</span> <span class="n">push</span><span class="p">(</span><span class="n">String</span> <span class="n">item</span><span class="p">)</span><span class="err">{</span></span>
<span class="code-line"> <span class="n">Node</span> <span class="n">nd</span> <span class="o">=</span> <span class="k">new</span> <span class="n">Node</span><span class="p">(</span><span class="n">item</span><span class="p">,</span><span class="k">first</span><span class="p">);</span></span>
<span class="code-line"> <span class="k">first</span> <span class="o">=</span> <span class="n">nd</span><span class="p">;</span></span>
<span class="code-line"> <span class="err">}</span></span>
<span class="code-line"> <span class="k">public</span> <span class="n">String</span> <span class="n">pop</span><span class="p">()</span><span class="err">{</span></span>
<span class="code-line"> <span class="n">String</span> <span class="n">firstItem</span> <span class="o">=</span> <span class="k">first</span><span class="p">.</span><span class="n">item</span><span class="p">;</span></span>
<span class="code-line"> <span class="k">first</span> <span class="o">=</span> <span class="k">first</span><span class="p">.</span><span class="k">next</span><span class="p">;</span></span>
<span class="code-line"> <span class="k">return</span> <span class="n">firstItem</span><span class="p">;</span></span>
<span class="code-line"> <span class="err">}</span></span>
<span class="code-line"> <span class="k">public</span> <span class="nb">boolean</span> <span class="n">isEmpty</span><span class="p">()</span><span class="err">{</span></span>
<span class="code-line"> <span class="k">return</span> <span class="k">first</span><span class="o">==</span><span class="k">null</span><span class="p">;</span></span>
<span class="code-line"> <span class="err">}</span></span>
<span class="code-line"><span class="err">}</span></span>
</pre></div>
</li>
<li>
<p>complexity: const time for every operation</p>
</li>
</ul>
<h3 id="array-implementation">array implementation</h3>
<ul>
<li>use array (of length N) to store items → defect: stack has limited capacity</li>
<li>
<p>keep a pointer *top: <strong>*pointing to the next empty space to push </strong>(top 的定义很重要)</p>
</li>
<li>
<p>problems of the array implementation: </p>
<ol>
<li>underflow: pop from an empty stack </li>
<li>overflow: size larger than capacity ⇒ resizing </li>
<li>
<p><strong>loitering</strong>: holding a ref to an obj which is no longer needed:
ex. <code>return s[top--]</code>
java system will not know that s[top] is no longer needed ⇒ have to clear it explicitely
⇒ </p>
<p>String item = s[top--];
s[top]=null;
return item</p>
</li>
</ol>
</li>
<li>
<p>implementation (containg resizing array operations) </p>
<div class="highlight"><pre><span class="code-line"><span></span><span class="k">public</span><span class="w"> </span><span class="k">class</span><span class="w"> </span><span class="n">ArrayStackOfStrings</span><span class="w"> </span><span class="n">implements</span><span class="w"> </span><span class="n">StackOfStrings</span><span class="err">{</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">private</span><span class="w"> </span><span class="n">String</span><span class="err">[]</span><span class="w"> </span><span class="n">s</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">private</span><span class="w"> </span><span class="nc">int</span><span class="w"> </span><span class="k">top</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">ArrayStackOfStrings</span><span class="p">()</span><span class="err">{</span><span class="o">//</span><span class="w"> </span><span class="k">to</span><span class="w"> </span><span class="n">be</span><span class="w"> </span><span class="n">tuned</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">String</span><span class="o">[</span><span class="n">1</span><span class="o">]</span><span class="p">;</span><span class="o">//</span><span class="n">initial</span><span class="w"> </span><span class="n">capacity</span><span class="o">=</span><span class="mi">1</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="err">}</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="k">boolean</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="err">{</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">top</span><span class="o">==</span><span class="mi">0</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="err">}</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">private</span><span class="w"> </span><span class="n">vois</span><span class="w"> </span><span class="n">resize</span><span class="p">(</span><span class="nc">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="err">{</span><span class="o">//</span><span class="n">helper</span><span class="w"> </span><span class="n">functoin</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">String</span><span class="err">[]</span><span class="w"> </span><span class="n">s2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">String</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">for</span><span class="p">(</span><span class="nc">int</span><span class="w"> </span><span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">i</span><span class="o"><</span><span class="k">top</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">s2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s2</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="err">}</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">item</span><span class="p">)</span><span class="err">{</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">if</span><span class="p">(</span><span class="k">top</span><span class="o">==</span><span class="n">s</span><span class="p">.</span><span class="n">length</span><span class="p">)</span><span class="o">//</span><span class="n">doubling</span><span class="w"> </span><span class="k">size</span><span class="w"> </span></span>
<span class="code-line"><span class="w"> </span><span class="n">resize</span><span class="p">(</span><span class="n">s</span><span class="p">.</span><span class="n">lenth</span><span class="o">*</span><span class="mi">2</span><span class="p">);</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">s</span><span class="o">[</span><span class="n">top++</span><span class="o">]=</span><span class="n">item</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="err">}</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="err">{</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">item</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="o">[</span><span class="n">--top</span><span class="o">]</span><span class="p">;</span><span class="o">//</span><span class="ow">NOT</span><span class="w"> </span><span class="k">top</span><span class="c1">--!</span></span>
<span class="code-line"><span class="w"> </span><span class="n">s</span><span class="o">[</span><span class="n">top</span><span class="o">]=</span><span class="k">null</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">if</span><span class="p">(</span><span class="k">top</span><span class="o">></span><span class="mi">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="k">top</span><span class="o">==</span><span class="n">s</span><span class="p">.</span><span class="n">length</span><span class="o">/</span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">//</span><span class="k">top</span><span class="o">></span><span class="mi">0</span><span class="w"> </span><span class="k">is</span><span class="w"> </span><span class="n">necessary</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">resize</span><span class="p">(</span><span class="n">s</span><span class="p">.</span><span class="n">length</span><span class="o">/</span><span class="mi">2</span><span class="p">);</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">item</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="err">}</span><span class="w"></span></span>
<span class="code-line"><span class="err">}</span><span class="w"></span></span>
</pre></div>
</li>
</ul>
<h1 id="2-resizing-arrays_1">2. Resizing Arrays</h1>
<p>resolving the overflow pb: grow and shrink the array
→ need to copy all items when changing array size
⇒ pb: <em>ensure that sizing happens infrequently</em></p>
<h3 id="resizing-strategy">resizing strategy</h3>
<ul>
<li>repeated doubling:</li>
</ul>
<p>(initial capacity=1) when array is full, double the size</p>
<ul>
<li><em>amortized</em> complexity for inserting N:</li>
</ul>
<p>N+(2+4+8+...+N) ~3N</p>
<ul>
<li>shrinking array</li>
</ul>
<p>⇒ shrink the array by half when array is <strong>1/4 full</strong>
not half full → <em>thrashing</em> will happen if push-pop-push-pop when array is full <br/>
<img alt="" class="img-responsive" src="../images/algoI_week2_1/pasted_image001.png"/> </p>
<ul>
<li><strong>[invariant]</strong>: array always 20%~100% full</li>
<li>complexity:</li>
</ul>
<p><em>in an amortized sense</em>, will be constant <br/>
<img alt="" class="img-responsive" src="../images/algoI_week2_1/pasted_image002.png"/> <br/>
<strong>proposition</strong>: from empty stack, M operations of push/pop taked time propotional to M</p>
<h3 id="comparison-resizable-array-vs-linkedlist">comparison: resizable array vs linkedlist</h3>
<ul>
<li>linkedlist implementation: </li>
</ul>
<p>operations takes const time even in worst time
extra time and space for dealing with linkes </p>
<ul>
<li>resizing array implementation:</li>
</ul>
<p>operation taked const <em>amortized</em> time
but in worst case takes linear time (ex. to be evited for critical systems)
less wasted space</p>
<h2 id="3-queues_1">3. Queues</h2>
<p>FIFO data structure
API</p>
<div class="highlight"><pre><span class="code-line"><span></span><span class="err">public interface QueueOfStrings{</span></span>
<span class="code-line"><span class="err"> void enqueue(String item);</span></span>
<span class="code-line"><span class="err"> String dequeue();</span></span>
<span class="code-line"><span class="err"> boolean isEmpty();</span></span>
<span class="code-line"><span class="err"> //int size();</span></span>
<span class="code-line"><span class="err">}</span></span>
</pre></div>
<h3 id="linked-list-implementation">linked list implementation</h3>
<p>maintain <code>first</code> and <code>last</code> node pointers:
pointing to 2 points of queue (<code>first</code> for dequeue, <code>last</code> for enqueue ) <br/>
<img alt="" class="img-responsive" src="../images/algoI_week2_1/pasted_image003.png"/> <br/>
→ <em>take care of corner cases</em>:
- empty queue: first is null (and last is also null)
- just one item in queue: first and last <em>point to the same node</em>
(总之first和last的定义很重要)</p>
<div class="highlight"><pre><span class="code-line"><span></span><span class="err"> public class LinkedQueueOfStrings implements QueueOfStrings{</span></span>
<span class="code-line"><span class="err"> class Node{... }</span></span>
<span class="code-line"><span class="err"> private Node first,last;</span></span>
<span class="code-line"><span class="err"> public LinkedQueueOfStrings(){</span></span>
<span class="code-line"><span class="err"> first = null;</span></span>
<span class="code-line"><span class="err"> }</span></span>
<span class="code-line"><span class="err"> public void enqueue(String item){//same as push</span></span>
<span class="code-line"><span class="err"> Node nd = new Node(item,null);</span></span>
<span class="code-line"><span class="err"> if(isEmpty()){</span></span>
<span class="code-line"><span class="err"> last = nd;</span></span>
<span class="code-line"><span class="err"> first = last;</span></span>
<span class="code-line"><span class="err"> }</span></span>
<span class="code-line"><span class="err"> else{</span></span>
<span class="code-line"><span class="err"> last.next = nd;</span></span>
<span class="code-line"><span class="err"> last = nd;</span></span>
<span class="code-line"><span class="err"> }</span></span>
<span class="code-line"><span class="err"> }</span></span>
<span class="code-line"><span class="err"> public String dequeue(){//same as pop in stack</span></span>
<span class="code-line"><span class="err"> String firstItem = first.item;</span></span>
<span class="code-line"><span class="err"> first = first.next;</span></span>
<span class="code-line"><span class="err"> if(isEmpty())</span></span>
<span class="code-line"><span class="err"> last=null;</span></span>
<span class="code-line"><span class="err"> return firstItem;</span></span>
<span class="code-line"><span class="err"> }</span></span>
<span class="code-line"><span class="err"> public boolean isEmpty(){</span></span>
<span class="code-line"><span class="err"> return first==null;</span></span>
<span class="code-line"><span class="err"> }</span></span>
<span class="code-line"><span class="err"> }</span></span>
</pre></div>
<h3 id="resizing-array-implementation">resizing array implementation</h3>
<p>maintain <code>head</code> and <code>tail</code>:
<code>head</code> is the queue head, <code>tail</code> is the <em>next empty position</em> for the next element to enqueue
→ trick: head and tail should take <em>mod capacity + </em>resizing array <br/>
<img alt="" class="img-responsive" src="../images/algoI_week2_1/pasted_image004.png"/> <br/>
不知道写的对不对: </p>
<div class="highlight"><pre><span class="code-line"><span></span><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="k">class</span><span class="w"> </span><span class="n">ArrayQueueOfStrings</span><span class="w"> </span><span class="n">implements</span><span class="w"> </span><span class="n">QueueOfStrings</span><span class="err">{</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">private</span><span class="w"> </span><span class="n">String</span><span class="err">[]</span><span class="w"> </span><span class="n">q</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">private</span><span class="w"> </span><span class="n">head</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="n">tail</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">LinkedQueueOfStrings</span><span class="p">()</span><span class="err">{</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">q</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">String</span><span class="o">[</span><span class="n">1</span><span class="o">]</span><span class="p">;</span><span class="o">//</span><span class="n">init</span><span class="w"> </span><span class="n">capacity</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="err">}</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="k">boolean</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="err">{</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">head</span><span class="o">==</span><span class="n">tail</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="err">}</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">private</span><span class="w"> </span><span class="n">void</span><span class="w"> </span><span class="n">resize</span><span class="p">(</span><span class="n">newsz</span><span class="p">)</span><span class="err">{</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">q2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">String</span><span class="o">[</span><span class="n">newsz</span><span class="o">]</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="nc">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="p">,</span><span class="n">j</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">while</span><span class="p">(</span><span class="n">i</span><span class="o">!=</span><span class="n">tail</span><span class="p">)</span><span class="err">{</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">q2</span><span class="o">[</span><span class="n">j++</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">q</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">i</span><span class="o">=</span><span class="p">(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">%</span><span class="n">q</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="err">}</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">q</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">q2</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">head</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">tail</span><span class="o">=</span><span class="n">j</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="err">}</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">void</span><span class="w"> </span><span class="n">enqueue</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">item</span><span class="p">)</span><span class="err">{</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">if</span><span class="p">(</span><span class="w"> </span><span class="p">(</span><span class="n">tail</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">%</span><span class="n">q</span><span class="p">.</span><span class="n">length</span><span class="o">==</span><span class="n">head</span><span class="w"> </span><span class="p">)</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">resize</span><span class="p">(</span><span class="n">q</span><span class="p">.</span><span class="n">length</span><span class="o">*</span><span class="mi">2</span><span class="p">);</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">q</span><span class="o">[</span><span class="n">tail</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">item</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">tail</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">tail</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">%</span><span class="n">q</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="err">}</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">dequeue</span><span class="p">()</span><span class="err">{</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">firstItem</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">q</span><span class="o">[</span><span class="n">head</span><span class="o">]</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">%</span><span class="n">q</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="nc">int</span><span class="w"> </span><span class="n">sz</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">tail</span><span class="o">-</span><span class="n">head</span><span class="p">)</span><span class="o">%</span><span class="n">q</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">if</span><span class="p">(</span><span class="n">sz</span><span class="o">></span><span class="mi">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">sz</span><span class="o">==</span><span class="n">q</span><span class="p">.</span><span class="n">length</span><span class="o">/</span><span class="mi">4</span><span class="p">)</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="n">resize</span><span class="p">(</span><span class="n">s</span><span class="p">.</span><span class="n">length</span><span class="o">/</span><span class="mi">2</span><span class="p">);</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">firstItem</span><span class="p">;</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="err">}</span><span class="w"></span></span>
<span class="code-line"><span class="w"> </span><span class="err">}</span><span class="w"></span></span>
</pre></div>
<h1 id="4-generics_2">4. Generics</h1>
<p>queues/stacks for other types of data ⇒ <em>generics 泛型</em>(java 1.5 才引进泛型机制...)
use <em>type paramater</em>→ avoid casting, and discover type mismatch errors <em>at compile time</em> </p>
<div class="highlight"><pre><span class="code-line"><span></span><span class="err"> public interface Stack<Item>{</span></span>
<span class="code-line"><span class="err"> public void push(Item item);</span></span>
<span class="code-line"><span class="err"> public Item pop();</span></span>
<span class="code-line"><span class="err"> public boolean isEmpty();</span></span>
<span class="code-line"><span class="err"> }</span></span>
</pre></div>
<h3 id="a-pb-with-array-implementation">a pb with array implementation</h3>
<p><strong>java不支持创立泛型数组</strong>
generic array creation is not allowed. 不可以new 一个泛型数组!
<code>s = new Item[capacity];</code>会报错 <br/>
⇒ use an ugly <em>cast</em>:
<code>s = (Item[]) new Object[capacity];</code>
(will get warning: "unchecked cast" → java被黑了... )</p>
<h3 id="autoboxing-for-primitive-types">autoboxing for primitive types</h3>
<p>each primitive type has a <em>wrapper class</em>
ex. int ↔ Integer
autoboxing: automatic cast between a primitive type and its wrapper class. <br/>
<img alt="" class="img-responsive" src="../images/algoI_week2_1/pasted_image005.png"/> <br/>
(syntactic sugar 语法糖 i.e. 对语言功能没有影响只是方便使用)<br/>
btw: <a href="https://zh.wikipedia.org/wiki/%E8%AF%AD%E6%B3%95%E7%B3%96">https://zh.wikipedia.org/wiki/%E8%AF%AD%E6%B3%95%E7%B3%96</a> (居然还有语法盐和语法糖精......)</p>
<h1 id="5-iterators_1">5. Iterators</h1>
<h3 id="interface">Interface</h3>
<p>support iteration over stacks and queues, <em>without revealing the internal representation</em> of stack/queue
⇒ implement the <code>Iterable</code> interface</p>
<ul>
<li>
<p><code>Iterable</code> interface: can return an *Iterator *</p>
<div class="highlight"><pre><span class="code-line"><span></span><span class="err">public interface Iterable{</span></span>
<span class="code-line"><span class="err"> Iterator<Item> iterator();</span></span>
<span class="code-line"><span class="err">}</span></span>
</pre></div>
</li>
<li>
<p>Iterator interface: hasNext() and next() interface</p>
<div class="highlight"><pre><span class="code-line"><span></span><span class="err">public interface Iterator<Item>{</span></span>
<span class="code-line"><span class="err"> boolean hasNext();</span></span>
<span class="code-line"><span class="err"> Item next();</span></span>
<span class="code-line"><span class="err"> void remove();//optional, bad practice to use it</span></span>
<span class="code-line"><span class="err">}</span></span>
</pre></div>
</li>
<li>
<p>to make a data structure Interable → elegant client code </p>
</li>
</ul>
<p><img alt="" class="img-responsive" src="../images/algoI_week2_1/pasted_image006.png"/> <br/>
<strong>how-to:</strong></p>
<ol>
<li>implement <code>Iterable</code> interface</li>
<li>write a <em>private inner class</em> XXIterator that implment the <code>Iterator</code> interface.</li>
</ol>
<p>ex. <br/>
<img alt="" class="img-responsive" src="../images/algoI_week2_1/pasted_image007.png"/> </p>
<h3 id="bag-data-structure">Bag data structure</h3>
<p>Supports adding and iterating through without caring about the order.<br/>
API: </p>
<div class="highlight"><pre><span class="code-line"><span></span><span class="err"> public class<Item> Bag implements Iterable<Item>{</span></span>
<span class="code-line"><span class="err"> public void add(Item);</span></span>
<span class="code-line"><span class="err"> int size(); </span></span>
<span class="code-line"><span class="err"> }</span></span>
</pre></div>
<p>can be implemented by stack or queue(without pop/dequeue)</p>
<h1 id="6-applications_1">6. Applications</h1>
<h3 id="java-collections-library">Java collections library</h3>
<p>List interface: <code>java.util.List</code> <br/>
<img alt="" class="img-responsive" src="../images/algoI_week2_1/pasted_image008.png"/> <br/>
implementations: <code>ArrayList</code>, <code>LinkedList</code>. </p>
<ul>
<li>pb with the java's implementation of stacks and queues: </li>
</ul>
<p><code>Stack</code> class also implements List interface (<code>get()</code>, <code>remove()</code>, <code>contains()</code> are implemented);<br/>
<code>Queue</code> is an interface rather than a class...<br/>
⇒ <strong>poorly designed API </strong></p>
<h3 id="stacks-applications">Stacks applications</h3>
<ul>
<li>function calls: </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/algoI_week2_1/pasted_image009.png"/> <br/>
recursion: can always use an explicit stack to remove recursion</p>
<ul>
<li>arithemic evaluation (Dijkstra) </li>
</ul>
<p>四种类型: 左括号, 右括号, 数字, 算子 <br/>
<img alt="" class="img-responsive" src="../images/algoI_week2_1/pasted_image010.png"/><br/>
最后一行应该是value stack. <br/>
<img alt="" class="img-responsive" src="../images/algoI_week2_1/pasted_image011.png"/> </p>
<p>⇒ 后缀表达式, 逆波兰式......</p>
</div>
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<div id="toc"><ul><li><a class="toc-href" href="#1-stacks" title="1. Stacks">1. Stacks</a><ul><li><a class="toc-href" href="#implementation-1-using-a-linkedlist" title="implementation 1: using a linkedlist">implementation 1: using a linkedlist</a></li><li><a class="toc-href" href="#array-implementation" title="array implementation">array implementation</a></li></ul></li><li><a class="toc-href" href="#2-resizing-arrays_1" title="2. Resizing Arrays">2. Resizing Arrays</a><ul><li><a class="toc-href" href="#resizing-strategy" title="resizing strategy">resizing strategy</a></li><li><a class="toc-href" href="#comparison-resizable-array-vs-linkedlist" title="comparison: resizable array vs linkedlist">comparison: resizable array vs linkedlist</a></li><li><a class="toc-href" href="#3-queues_1" title="3. Queues">3. Queues</a><ul><li><a class="toc-href" href="#linked-list-implementation" title="linked list implementation">linked list implementation</a></li><li><a class="toc-href" href="#resizing-array-implementation" title="resizing array implementation">resizing array implementation</a></li></ul></li></ul></li><li><a class="toc-href" href="#4-generics_2" title="4. Generics">4. Generics</a><ul><li><a class="toc-href" href="#a-pb-with-array-implementation" title="a pb with array implementation">a pb with array implementation</a></li><li><a class="toc-href" href="#autoboxing-for-primitive-types" title="autoboxing for primitive types">autoboxing for primitive types</a></li></ul></li><li><a class="toc-href" href="#5-iterators_1" title="5. Iterators">5. Iterators</a><ul><li><a class="toc-href" href="#interface" title="Interface">Interface</a></li><li><a class="toc-href" href="#bag-data-structure" title="Bag data structure">Bag data structure</a></li></ul></li><li><a class="toc-href" href="#6-applications_1" title="6. Applications">6. Applications</a><ul><li><a class="toc-href" href="#java-collections-library" title="Java collections library">Java collections library</a></li><li><a class="toc-href" href="#stacks-applications" title="Stacks applications">Stacks applications</a></li></ul></li></ul></div>
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